# Particle size distribution/histogram errors.

• RossJJ
In summary, your supervisor is asking you to use the technique of propagation of error to account for the errors in your data and obtain an estimate of the uncertainty associated with each bin in your histogram.
RossJJ
I posted this elsewhere but probably in the wrong topic so have reposted here.

Okay, so I have obtained a particle size distribution of diesel exhaust particles on a SEM. Data has been plotted and fitted with a lognormal distribution. Although it isn't a usual path to take I have been told I must put errors on each bin height. I obviously have an error on each individual particle measurement but I am having issues converting this to an error in the frequency counts/probability.
I tried to take the errors and re-bin the particles with the error added and subtracted but was told I should follow the usual error procedure, such as adding in quadrature or something similar, other than that my supervisor was quite vague.
After many a trawl of articles and suchlike I am coming up blank, mainly because it is rather rare to use errors on a histogram, as a histogram is kind of inherent of the errors, being a distribution and whatnot.

It sounds like your supervisor is asking you to use a method known as propagation of error, or uncertainty propagation. This is a common technique used in statistics when dealing with data that has errors associated with it. The idea is to propagate the errors from the individual measurements up to the final result. In your case, you would need to calculate the uncertainty associated with each bin in the histogram. You can do this by propagating the errors in the individual particle measurements through any calculations you have done to obtain the frequency counts and/or probabilities for each bin. This will give you an estimate of the uncertainty associated with each bin.For more information on propagation of error and how to calculate it, you may want to search online for tutorials or guides on the subject.

## 1. What is particle size distribution?

Particle size distribution refers to the measurement of the size of particles in a sample. It is often represented by a graph or histogram that shows the number or percentage of particles at different size ranges.

## 2. Why is particle size distribution important?

Particle size distribution is important in various industries, such as pharmaceuticals, cosmetics, and environmental monitoring. It can affect the physical and chemical properties of a product, as well as its performance and stability.

## 3. What are some common errors in particle size distribution/histogram analysis?

Some common errors in particle size distribution analysis include improper sample preparation, instrument malfunction, and human error in data interpretation. Additionally, the choice of measurement technique and data processing can also lead to errors in the final results.

## 4. How can I minimize errors in particle size distribution analysis?

To minimize errors in particle size distribution analysis, it is important to carefully follow the sample preparation instructions and ensure that the instrument is properly calibrated and functioning correctly. Using multiple measurement techniques and validating results can also help reduce errors.

## 5. How can particle size distribution analysis be used in quality control?

Particle size distribution analysis is a useful tool in quality control as it can help ensure consistency and uniformity in products. By regularly monitoring particle size distribution, manufacturers can identify any variations or errors in their processes and make necessary adjustments to maintain product quality.

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